Rpv session 1

CAT
Concept Session 1: Ratio, Proportion and Variation
www.georgeprep.com 9985-372-371

Session 1
Ratio – Introduction and Terminology
Ratio - Properties
Combining ratios
Proportion – Properties
Session 2
Variation – Properties
Comparison of fractions – Part 1
Comparison of fractions – Part 2
Problem Set – 1
Problem Set -2
Ratio, Proportion and variation

Ratio, Proportion and Variation – Session 1
• Ratio – Introduction and Terminology

Ratio – What is it?
 Ratio: Comparison of magnitude of two quantities.
The ratio of the expenses of A and B is 5:9. If the sum of their
expenses is Rs. 28000.
- What is A’s expense?
- By how much is B’s expense greater than A’s expense?

Ratio – Problems on basic understanding
What is the value of A:B:C ? If,
a) A:B:C =
1
3
∶
1
2
∶
1
5
b)
A
3
=
B
2
=
C
5

Ratio – Terminology
 Terminology
 Antecedent and consequent
 Let the ratio of A’s age and B’s age = a:b and B’s age and C’s age = b:c
 Duplicate ratio of their ages =
 Triplicate ratio of their ages =
 Sub-duplicate ratio of their ages =
 Sub-triplicate ratio of their ages =

Ratio – Terminology
⁻ If 5a+2 : 12a+4 is the triplicate ratio of 3:4, what is the value of a?

• Ratio – Properties

Ratio – Properties
Properties of Ratios
Value of ratios when multiplied or divided by the same number remains the
same

Change of values of proper and improper fractions when the same value is added or subtracted
to the Nr and the Dr.
Proper Fraction Improper Fraction

If
𝑎
𝑏
=
𝑐
𝑑
=
𝑒
𝑓
……. then
𝑎 + 𝑐 + 𝑒 +⋯
𝑏+𝑑+𝑓+⋯
= each of
𝑎
𝑏
,
𝑐
𝑑
… As long as (𝑏 +
𝑑 + 𝑓 + ⋯ ) ≠ 0

• Given
𝑎
𝑏
,
𝑐
𝑑
,
𝑒
𝑓
, the value of
𝑎+𝑐+𝑒
𝑏+𝑑+𝑓
will be between the lowest and highest fraction.

Properties of Ratios - Summary
• Value of ratios when multiplied or divided by the same number remains the
same
• Change of values of proper and improper fractions when the same value is
added or subtracted to the Nr and the Dr.
• If
𝑎
𝑏
=
𝑐
𝑑
=
𝑒
𝑓
……. then
𝑎 + 𝑐 + 𝑒 +⋯
𝑏+𝑑+𝑓+⋯
= each of
𝑎
𝑏
,
𝑐
𝑑
… As long as (𝑏 + 𝑑 + 𝑓 + ⋯ ) ≠
0
• Given
𝑎
𝑏
,
𝑐
𝑑
,
𝑒
𝑓
, the value of
𝑎+𝑐+𝑒
𝑏+𝑑+𝑓
will be between the lowest and highest fraction.

If
𝑎+𝑏
𝑐
=
𝑏+𝑐
𝑎
=
𝑎+𝑐
𝑏
= p, what is the value of p?
1) 2 2) -1 3) -2 4) Either 1) or 2)

• Combining Ratios

Ratio – Combining ratios

Ratio – Problems
If A:B = 3:1, C:B = 2:1, C:D = 1:3 what is the value of A:D?
1) 1:2 2) 2:1 3) 1:3 4) None of these

Ratio – Problems
A has thrice the amount of money that B has, B has twice
the amount of money that C has and thrice the amount of
money with C is equal to four times the amount of money
with D. The amount of money with D is what percentage of
the amount of money with A?
1) 200 2) 25 3) 12.5 4) None of these

• Proportion – Properties

Proportion – What is it?
 What is a proportion?
 Product of extremes = product of means

Proportion – Continued Proportion
 If a:b =b:c, then a,b and c are in continued proportion.

Proportion – Properties
 Invertendo
 Alternendo
 Componendo
 Dividendo
 Componendo-dividendo

Proportion – Problems
Ratio of p:q is the same as that of q:r, where p, q and r are
positive numbers. If p = 16 and r = 100, find q.
1) 40 2) 64 3) 24 4) None of these

Proportion – Problems
Find the fourth proportional to 1, 3 and 4
1) 12 2) 24 3) 18 4) None of these

Rpv session 1

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